Analysis of genotype by methylation interactions through sparsity-inducing regularized regression

In this paper, we consider the use of the least absolute shrinkage and selection operator (LASSO)-type regression techniques to detect important genetic or epigenetic loci in genome-wide association studies (GWAS) and epigenome-wide association studies (EWAS). We demonstrate how these techniques can be adapted to provide quantifiable uncertainty using stability selection, including explicit control of the family-wise error rate. We also consider variants of the LASSO, such as the group LASSO, to study genetic and epigenetic interactions. We use these techniques to reproduce some existing results on the Genetics of Lipid Lowering Drugs and Diet Network (GOLDN) data set, which collects from 991 individuals blood triglyceride and differential methylation at 464,000 cytosine-phosphate-guanine (CpG) sites and 761,000 single-nucleotide polymorphisms (SNPs), and to identify new research directions. Epigenome-wide and genome-wide models based on the LASSO are considered, as well as an interaction model limited to chromosome 11. The analyses replicate findings concerning 2 CpGs in carnitine palmitoyltransferase 1A (CPT1A). Some suggestions are made regarding potentially interesting directions for the analysis of genetic and epigenetic interactions.